What is "law of the excluded middle"

Contradiction \Con`tra*dic"tion\, n. [L. contradictio answer, objection: cf. F. contradiction.]

1. An assertion of the contrary to what has been said or affirmed; denial of the truth of a statement or assertion; contrary declaration; gainsaying.

   His fair demands Shall be accomplished without contradiction.
   --Shak.

2. Direct opposition or repugnancy; inconsistency; incongruity or contrariety; one who, or that which, is inconsistent.

   can he make deathless death? That were to make Strange contradiction.
   --Milton.

   We state our experience and then we come to a manly resolution of acting in contradiction to it.
   --Burke.

   Both parts of a contradiction can not possibly be true.
   --Hobbes.

   Of contradictions infinite the slave.
   --Wordsworth.

   Principle of contradiction (Logic), the axiom or law of thought that a thing cannot be and not be at the same time, or a thing must either be or not be, or the same attribute can not at the same time be affirmed and and denied of the same subject; also called the law of the excluded middle.

   Note: It develops itself in three specific forms which have been called the ``Three Logical Axioms.'' First, ``A is A.'' Second, ``A is not Not-A'' Third, ``Everything is either A or Not-A.''

n. (alternative form of law of excluded middle English)